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Chapter 5: Q. 280 (page 672)

In the following exercises, determine whether each ordered pair is a solution to the system.

6x-5y<20-2x+7y>-8a.(1,-3b.(-4,4)

Short Answer

Expert verified

Part (a) The ordered pair is not a solution to the set.

Part (b) The ordered pair is a solution to the set.

Step by step solution

01

Part a. Step 1. Given Information

The given set is 6x-5y<20-2x+7y>-8and the ordered pair is(1,-3).

02

Part a. Step 2. Substitute the values into the inequalities. 

  • Substitute x=1,y=-3into the first given inequality.

6(1)-5(-3)<?206+15<?2021<20False

  • Substitute into the second inequality.

-2(1)+7(-3)>?-8-2-21>?-8-23>-8False

  • Since both of the inequalities are not satisfied, the given ordered pair is not a solution to the system.
03

Part b. Step 1. Given Information

The given set is6x-5y<20-2x+7y>-8and the ordered pair is(-4,4).

04

Part b. Step 2. Substitute the values into the inequalities   

  • Substitute x=-4,y=4into the first given inequality.

6(-4)-5(4)<?20-24-20<?20-44<20True

  • Substitute x=4,y=-4into the second given inequality.

-2(-4)+7(4)>?-88+28>?-836>-8True

  • Since both of the inequalities are satisfied, the given ordered pair is a solution to the system.

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